What does the narrator want to teach Doodle to do next? From whom does he keep this plan a secret?
The narrator teaches Doodle to walk without telling anyone; after Doodle can walk, he brings Doodle to the door near the dining room and has Doodle demonstrate. After this success, the brother decides that he will teach Doodle to run and more. Naturally, he keeps this secret from everyone else in the family: Mama and Daddy, and Aunt Nicey.
I would teach him to run, to swim, to climb trees, and to fight. He, too, now believed in my infallibility, so we set the deadline for these accomplishments less that a year away, when ... Doodle could start to school.
Because the brother keeps his plans from the other members of his family, there is no one to reign him in and tell him that his goals for Doodle are unrealistic. The narrator, who "began to believe in [his] own infallibility," is motivated to push his brother into running and the rest because of his own pride--"I should have already admitted defeat, but my pride wouldn't let me"--just as he was motivated in teaching his brother to walk. In a sense, the brother is very selfish as he has not wanted to be embarrassed by his little brother, Doodle, whose development has been slow. He also is unrealistic, believing less in Doodle, but more in his "infallibility." Tragically, he is later punished for his selfishness and what he calls "a knot of cruelty borne by the stream of love."